# Particular Correlation formula

I'm reading a book where the autocorrelation of white noise is expressed as:

What is the term $$Q(k)$$ and why is is expressed as an average value of a dot product ?

• That's not an average, that's an expectation operator! Anyway, that's really a topic for a different day. $Q$ is probably just the covariance matrix, and it's likely defined somewhere around this? – Marcus Müller Feb 9 '19 at 10:03

I’m guessing your book is on Kalman filters and $$u(k)$$ is a term in a state variable equation of a linear system. If so, it is a vector and the components of that vector at some time index $$k$$ can be correlated with each other but are independent with respect to $$k$$.